Convergence Analysis of Adaptive Exponential Functional Link Network

The adaptive exponential functional link network (AEFLN) is a recently introduced novel linear-in-the-parameters nonlinear filter and is used in numerous nonlinear applications, including system identification, active noise control, and echo cancellation. The improved modeling accuracy offered by AEFLN for different nonlinear applications can be attributed to the exponentially varying sinusoidal basis functions used for nonlinear expansion. Even though AEFLN has been widely used for the identification of nonlinear systems, no theoretical analysis of AEFLN is available in the literature. Hence, in this article, a theoretical performance analysis of AEFLN trained using an adaptive exponential least mean square (AELMS) algorithm under the Gaussian input assumption is discussed. Expressions describing the mean as well as mean square behavior of the weight vector and adaptive exponential parameter are derived. Computer simulations are carried out, and the derived theoretical expressions show a close correspondence with simulation results.